If we're looking at the capabilities of the character itself, then the face value capabilities of the same-class multiclasses that you requested are as follows:
At level one, a Fighter gets a bonus feat, and nothing more. If the character were to keep taking a level one Fighter each level, then over the course of the development the character would on average gain 1.5 feats per level instead of 1 and would have full BAB, but no bonus to non Fortitude saves and any other feature of the Fighter. Seeing as Fighters already have a great many feats, having even more at the cost of normal Fighter advancement skills seems woefully underpowered.
As mentioned earlier, Wizards would in theory get more of their tangibles from selecting the same class. I can't speak to the potential power of having multiple bonded items or familiars as I am not a Wizard player, but the early game money from cycling the spellbooks and the vast number of low level spells per day seems overshadowed by the drawback of not getting higher levels spells quicker. Not to mention, as only one Wizard class could be leveled at a time, in the long run only one familiar would be particularly useful. The other would fall off very hard.
While a player may be able to select multiple domains, they would only reap the benefits of how much they leveled each Cleric due to the powers obtained through progression. On top of this, Channeled Energy does not stack between classes, so even if a player wanted to enhance both Clerics, or however many he has, his Channeled Energy power would never surpass that dictated by his highest Cleric level.
The only benefit to this would be extra sneak attack damage early. Unless one really cares about having 2d6 sneak attack at level 2 instead of 3, this seems completely worthless because rogue talents don't come into play until level 2.
In general, it seems like a strategy like this is quite weak due to the fact that any early benefits are neutered in the long term because there's no progression on them. Perhaps there's more abuse potential if the campaign is short and the characters don't advance greatly, but that might have to be play-tested. I think archetypes would also be affected the same way as the normal classes due to the progression issue.
If I were a GM, I would probably prohibit this style of leveling not because of the abuse, but because I can't see a way that a player wouldn't be setting themselves up for a disappointment.